A protest in Lahore last week against the release of Asia Bibi.
Photograph: Rahat Dar/EPA

The family of Asia Bibi, the Christian woman who spent eight years on death row in Pakistan for blasphemy before being acquitted three weeks ago, claim they are being hunted by extremists going house to house with their photographs to try to track them down.

Bibi’s family have been in hiding since her acquittal by the country’s supreme court. She is in protective custody as part of a deal between the government and a hardline Islamic party, under which violent protests were called off while a review of the court ruling was undertaken.

Bibi’s lawyer, relatives and supporters have appealed for the family to be given asylum in a European or north American country. Several countries have indicated their willingness to offer a home, but nothing concrete has emerged.

John Pontifex, of Aid to the Church in Need UK (ACN), which has campaigned on Bibi’s behalf since she was convicted and sentenced to death in 2010, said he had been in almost daily contact with her family over the past three weeks and they were very frightened.

“They have told me that mullahs had been reported in their neighbourhood going from house to house showing photos of family members on their phones, trying to hunt them down,” he told the Guardian.

“The family have had to move from place to place to avoid detection. Sometimes they can only operate after sundown. They have had to cover their faces when they go out in public. They have had to remove the rosary that hangs from their car rear-view mirror for fear of attack.”

Pontifex said the family’s faith was “sustaining them in this time of acute danger”. He added: “They say that if they are not allowed to find a future outside Pakistan, the fear is that sooner or later something terrible might happen to them.”

Bibi’s lawyer, who fled Pakistan shortly after the court ruling saying his life was in danger, said this week that talks on asylum were under way with several European countries. “I hope the western world is trying to help her,” Saiful Malook told reporters in Frankfurt.

Canada, Spain and France are thought to have offered asylum to Bibi. Germany and Italy have reportedly held talks with Pakistan on the issue.

The UK government has declined to answer questions about whether it is considering an offer of asylum, saying it does not want to further endanger Bibi and her family.

The former foreign secretary Boris Johnson and many other MPs and peers have called for the UK government to act. Some reports have suggested that the government fears a backlash among British Muslims of Pakistani heritage if it offers Bibi asylum.

On Tuesday, Sayeeda Warsi told the House of Lords: “There have been press reports that Asia Bibi, if granted asylum in the United Kingdom, would potentially not be safe from some communities here … As someone who is deeply connected to British Muslim communities, I assure her that they are fully supportive of any asylum claim that Asia Bibi may have and that our country may afford her, and that she would be supported as she would be by all other communities in this country.”

The Muslim Council of Britain said in a tweet: “There are unfounded media reports that Pakistani national Asia Bibi is being denied asylum into the UK because of concerns from British Muslims. We find such insinuations to be as nonsensical as they are divisive. We see no reason why Asia Bibi should be denied asylum into the UK.”

After Bibi’s acquittal, Islamic hardliners called for her and the judges in the case to be killed, and they mounted protests that brought cities to a standstill. Pakistan’s prime minister, Imran Khan, has been accused of capitulating to their demands.

Bibi, a farm labourer, was accused by Muslim villagers of insulting the prophet Muhammad in a row over a cup of water. The supreme court judgment said there was no evidence to support the charge.